ximations are accepted and a completely rigorous solution is disregarded in favour of a some 
what simpler treatment. The leading idea then is to work with independent units which undergo 
no other alterations or deformations than by transformation (including non-linear transforma 
tion). Independent models (stereopairs) are the most familiar example. The choice of suitable 
units must not only consider the computing technique, but should rather be based on the feasi 
bility from the photogrammetric point of view. In case units are chosen whose approximations 
go too far (whose internal residual errors cannot be tolerated) it is difficult to rectify the over 
simplification, at least with direct solution procedures. Application of relaxation techniques 
might again still be feasible, however. 
At present the main concentration seems to be on adjustment procedures based on the 
treatment of independent models (as a special case of independent sections). The approxima 
tions are very small compared with the ideal single plates approach. A theoretical investiga - 
tion into the effect of the approximation is, however, still missing. Mathematical formulations 
of the model approach are given in [7 0], [74], [75], [83] - [86]. The use of models as basic ad 
justment units has the advantage that its application is not restricted to comparator measure - 
ments and also that models measured in any stereo-restitution instrument can go into the block- 
adjustment directly. Finally, but certainly not the least practical advantage, is the fact that the 
adjusted units are directly suited for subsequent plotting. Under the influence of this kind of 
block-adjustment the conventional strip-triangulation and hence the first order instruments 
seem to loose importance in favour of measurement of independent models in second order ins 
truments supplied with coordinate registration equipment. 
The obvious successes of the model approach of block-adjustment reduce the practical 
importance of those block-adjustment procedures which work with polynomial corrections for 
strips and which are labeled as distinctly approximate. This is especially true since in both 
cases middle class computers are suited and the amount of computing required is apparently of 
a similar order of magnitude. Hence the interest in less accurate and less general applicable 
polynomial procedures will probably decrease in future. 
*3. 5 Regarding the task of numerical solution of block-adjustment it is remarkable that all 
theoretical approaches based on any form of independent units lead essentially to the same type 
of computing problem. The number of units may be different but the common problem is to 
connect them by taking into account all mutual interrelations. It can be shown that the various 
approaches give, or can be reduced to, systems of equations of siriiilar structure. The non 
zero terms of the equations to be solved can be arranged to form a band along the principal dia 
gonal of the coefficient matrix. The width of the band is determined by the number of units 
which are directly interconnected. In [86] the author has shown the structural identity of the 
normal equations or partially reduced normal equations of some approaches. This property is 
even independent of the actual choice of the unknowns. 
All considerations about the principles of numerical solution of block-adjustment start 
from the basic fact that the number of unknowns to be determined is usually rather large (or - 
der of magnitude 10^ - 10^ ). The great number of solution techniques available can be classi 
fied in a few groups : 
a) The direct solution working with an elimination procedure according to the Gauss algorith- 
me or other equivalent reduction techniques. It seems that the direct solution has received lit 
tle attention, probably because of apparent storage requirements. Only the ITC procedure fol 
lows at present this line. The existence of a direct solution which can favourably compete with 
other solutions might influence the future development. 
b) The iterative solution of a large number of equations seems in general to be the most attrac 
tive procedure both for large and medium size computers. With iterative solutions the problem 
of convergence arises. In blocks with little ground control the convergence is slow. The Ord 
nance survey and others ( [56], [7 0] ) have collected experimental information about the rate of 
convergence of iterative solutions for the block sizes normally encountered. The drawback of 
it is that the results of experiments are only to be trusted within the range investigated but are 
still not sufficiently informative about unusual cases. Miles [85] has referred to a theoretical